# How do you find the sum of Sigma [(i-1)^2+(i+1)^3] where i is [1,4]?

Nov 13, 2017

$238$

#### Explanation:

${\sum}_{i = 1}^{4} \left[{\left(i - 1\right)}^{2} + {\left(i + 1\right)}^{3}\right]$

$= {\sum}_{i = 1}^{4} \left({i}^{2} - 2 i + 1 + {i}^{3} + 3 {i}^{2} + 3 i + 1\right)$

$= {\sum}_{i = 1}^{4} \left({i}^{3} + 4 {i}^{2} + i + 2\right)$

$= {\left(\frac{4 \cdot 5}{2}\right)}^{2} + 4 \cdot \frac{4 \cdot 5 \cdot 9}{6} + \frac{4 \cdot 5}{2} + 2 \cdot 4$

$= 238$